This article provides three new forms of convergence, namely, \(\mathcal {I}^*_{\alpha }\) -ue, \(\mathcal {I}^*_{\alpha }\) -ud and \(\mathcal {I}^*_{\alpha }\) -sue. We explore here a number of lattice features of the classes made up of all those real valued functions defined on a metric space, which are \(\mathcal {I}^*_{\alpha }\) -ue limits, \(\mathcal {I}^*_{\alpha }\) -ud limits and \(\mathcal {I}^*_{\alpha }\) -sue limits respectively for sequences of functions belong to a particular class. In addition, we define the term \(\mathcal {I}\alpha \) -equal convergence and follow up some associated findings.
